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Probability and natural deduction J. Log. Comput. (IF 0.7) Pub Date : 2024-03-06 Marija Boričić Joksimović, Nebojša Ikodinović, Nenad Stojanović
We develop a system of basic probability reasoning founded on two great logical concepts, Gentzen’s natural deduction systems and Carnap–Popper probability of sentences. Our system makes it possible to manipulate with probabilized sentences and justify their causal relationships: if probabilities of sentences $A$ and $B$ are in $[r,1]$ and $[s,1]$, respectively, then the probability of sentence $C$
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Congruence filter pairs, equational filter pairs and adjoints J. Log. Comput. (IF 0.7) Pub Date : 2024-02-26 Peter Arndt, Hugo Luiz Mariano, Darllan Conceição Pinto
Filter pairs are a tool for creating and analyzing logics. A filter pair can be seen as a presentation of a logic, given by presenting its lattice of theories as the image of a lattice homomorphism, with certain properties ensuring that the resulting logic is substitution invariant. Every substitution invariant logic arises from a filter pair. Particular classes of logics can be characterized as arising
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Modalities combining two negations J. Log. Comput. (IF 0.7) Pub Date : 2024-02-13 José Luis Castiglioni, Rodolfo C Ertola-Biraben
In the context of positive logic expanded with the dual of intuitionistic negation, obtaining intuitionistic negation itself as a consequence, those two connectives allow to introduce modal concepts such as necessity and possibility. We study the resulting modal logic, paying attention to different extensions of it. We provide a syntactic approach and both algebraic and Kripke semantics.
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Computably enumerable equivalence relations via primitive recursive reductions J. Log. Comput. (IF 0.7) Pub Date : 2024-01-31 Birzhan S Kalmurzayev, Nikolay A Bazhenov, Alibek M Iskakov
The complexity classification of computably enumerable equivalence relations (or ceers, for short) has received much attention in the recent literature. A measure of complexity is typically provided by an appropriate notion of a reduction. Given binary relations $R$ and $S$ on natural numbers, a total function $f$ is a reduction from $R$ to $S$ if for arbitrary $x$ and $y$, the conditions $x~R~y$ and
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On sheaves on semicartesian quantales and their truth values J. Log. Comput. (IF 0.7) Pub Date : 2024-01-22 Ana Luiza Tenorio, Caio de Andrade Mendes, Hugo Luiz Mariano
In this paper, we introduce a new definition of sheaves on semicartesian quantales, providing first examples and categorical properties. We note that our sheaves are similar to the standard definition of a sheaf on a locale; however, we prove that in general it is not an elementary topos—since the lattice of external truth values of $Sh(Q)$, $Sub(1)$, is canonically isomorphic to the quantale $Q$—placing
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Algorithmic properties of modal and superintuitionistic logics of monadic predicates over finite Kripke frames J. Log. Comput. (IF 0.7) Pub Date : 2024-01-15 Mikhail Rybakov, Dmitry Shkatov
We show that the monadic fragment of the modal predicate logic of a single Kripke frame with finitely many possible worlds, but possibly infinite domains, is decidable. This holds true even for multimodal logics with equality, regardless of whether equality is interpreted as identity or as congruence. By the Gödel–Tarski translation, similar results follow for superintuitionistic predicate logics,
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An encoding of abstract dialectical frameworks into higher-order logic J. Log. Comput. (IF 0.7) Pub Date : 2024-01-12 Antoine Martina, Alexander Steen
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant Isabelle/HOL. This approach allows for the computer-assisted analysis of abstract dialectical frameworks using automated and interactive reasoning tools within a uniform
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On the conservation results for local reflection principles J. Log. Comput. (IF 0.7) Pub Date : 2024-01-05 Haruka Kogure, Taishi Kurahashi
For a class $\varGamma $ of formulas, $\varGamma $ local reflection principle $\textrm{Rfn}_{\varGamma }(T)$ for a theory $T$ of arithmetic is a scheme formalizing the $\varGamma $-soundness of $T$. Beklemishev (1997, Theoria, 63, 139–146) proved that for every $\varGamma \in \{\varSigma _{n}, \varPi _{n+1} \mid n \geq 1\}$, the full local reflection principle $\textrm{Rfn}(T)$ is $\varGamma $-conservative
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Coarsening Natural Deduction Proofs I: Finding Perfect Proofs J. Log. Comput. (IF 0.7) Pub Date : 2024-01-03 Ethan Brauer
This paper explores how, given a proof, we can systematically transform it into a proof that contains no irrelevancies and which is as strong as possible. I define a weaker and stronger notion of what counts as a proof with no irrelevancies, calling them perfect proofs and gaunt proofs, respectively. Using classical core logic to study classical validities and core logic to study intuitionistic validities
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Numeral completeness of weak theories of arithmetic J. Log. Comput. (IF 0.7) Pub Date : 2023-12-14 Reinhard Kahle, Isabel Oitavem, Paulo Guilherme Santos
We study numeral forms of completeness and consistency for $\mathsf {S}^1_2$ and other weak theories, like $\mathsf {EA}$. This gives rise to an exploration of the derivability conditions needed to establish the mentioned results; a presentation of a weak form of Gödel’s Second Incompleteness Theorem without using ‘provability implies provable provability’; a provability predicate that satisfies the
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Hamilton’s cumular conception of quantifying particles: an exercise in third-order logic J. Log. Comput. (IF 0.7) Pub Date : 2023-12-04 David Makinson
Sir William Hamilton is remembered for his proposal to extend the four traditional categoricals to eight by quantifying predicate as well as subject terms. He intended the quantifying particles to be understood in a ‘collective’ or ‘cumular’ manner rather than in a ‘distributive’ or ‘exemplar’ one, but commentators from De Morgan onwards have worked primarily from the latter perspective, comforted
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Defining Logical Systems via Algebraic Constraints on Proofs J. Log. Comput. (IF 0.7) Pub Date : 2023-11-27 Alexander V Gheorghiu, David J Pym
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof system for a target logic by enriching a proof system for another, typically simpler, logic with an algebra of constraints that act as correctness conditions on the latter
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Computational paths - a weak groupoid J. Log. Comput. (IF 0.7) Pub Date : 2023-11-24 Tiago M L de Veras, Arthur F Ramos, Ruy J G B de Queiroz, Anjolina G de Oliveira
On the basis of a labelled deduction system (LND$_{ED-}$TRS), we demonstrate how to formalize the concept of computational paths (sequences of rewrites) as equalities between two terms of the same type. This has allowed us to carry out a formal counterpart to equality between paths which is dealt with in homotopy theory, but this time with an approach using the device of term-rewriting paths. Using
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Applying Theory to Practice J. Log. Comput. (IF 0.7) Pub Date : 2023-11-22 Ronald Fagin
By making use of three IBM case studies involving the author and colleagues, this paper is about applying theory to practice. In the first case study, the system builders (or practitioners) initiated the interaction. This interaction led to the following problem. Assume that there is a set of objects, each with multiple attributes, and there is a numerical score assigned to each attribute of each object
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Context-based argumentation frameworks and multi-agent consensus building J. Log. Comput. (IF 0.7) Pub Date : 2023-10-20 Zhe Yu, Shier Ju, Weiwei Chen
Argumentation must be conducted within specific contexts that involve particular social norms and values. For decision-making, the divergence of opinions among participants does not lie solely in disagreements of common sense and beliefs but mainly stems from differences in the priority orderings over values. In this paper, we discuss how to build consensus among participants holding different value
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PubHubs identity management J. Log. Comput. (IF 0.7) Pub Date : 2023-10-18 Bart Jacobs, Bram Westerbaana, Omar Javed, Harm van Stekelenburg, Lian Vervoort, Jan den Besten
Finding a combination between privacy and accountability in the online world is a challenge. Too little accountability supports problematic behaviour. Too little privacy undermines individual freedom and has a chilling effect. This paper describes the identity infrastructure of a new open source community platform called PubHubs. It combines local group conversations, via its own adaptation of Matrix
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Polyhedral semantics and the tractable approximation of Łukasiewicz infinitely-valued logic J. Log. Comput. (IF 0.7) Pub Date : 2023-10-13 Marcelo Finger, Sandro Preto
In this work, we present polyhedral semantics as a means to tractably approximate Łukasiewicz infinitely-valued logic (Ł$_{\infty}$). As Ł$_{\infty}$ is an expressive multivalued propositional logic whose decision problem is NP-complete, we show how to to obtain an approximation for this problem providing a family of multivalued logics over the same language as Ł$_{\infty}$. Each element of the family
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Uncertainty-based knowing how logic J. Log. Comput. (IF 0.7) Pub Date : 2023-10-10 Carlos Areces, Raul Fervari, Andrés R Saravia, Fernando R Velázquez-Quesada
We introduce a novel semantics for a multi-agent epistemic operator of knowing how, based on an indistinguishability relation between plans. Our proposal is, arguably, closer to the standard presentation of knowing that modalities in classical epistemic logic. We study the relationship between this new semantics and previous approaches, showing that our setting is general enough to capture them. We
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Modeling dynamics of legal relations with dynamic logic J. Log. Comput. (IF 0.7) Pub Date : 2023-09-25 Jan van Eijck, Fengkui Ju, Tianwen Xu
The fundamental relations in private law are claims and duties. These legal relations can be changed by agents with the appropriate legal powers. We use propositional dynamic logic and ideas about propositional control from the agency literature to formalize these changes in legal relations. Our models are sets of states with functions specifying atomic facts, agents’ abilities to change atomic facts
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Modelling supra-classical logic in a Boltzmann neural network: III adaptation J. Log. Comput. (IF 0.7) Pub Date : 2023-09-01 Glenn Blanchette, Anthony Robins
The field of belief revision in logic is still in evolution and holds a variety of disparate approaches; a consequence of theoretical conjecture. As a probabilistic model of supra-classical, non-monotonic (SCNM) logic, the Boltzmann machine, offers an experimental gateway into the field. How does the Boltzmann network adapt to new information? Catastrophic forgetting is the default response to retraining
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Bisimulation in model-changing modal logics: An algorithmic study J. Log. Comput. (IF 0.7) Pub Date : 2023-08-25 Sujata Ghosh, Shreyas Gupta, Lei Li
We discuss the notion of bisimulation in various model-changing modal logics and provide an algorithmic study of the same. We provide a general algorithm which gives an overall procedure to check whether two models are bisimilar in all these logics. Through our algorithmic analyses we provide a PSPACE upper bound of the bisimulation/model comparison problem of all these modal logics. We also provide
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Linear logic in a refutational setting J. Log. Comput. (IF 0.7) Pub Date : 2023-08-13 Mario Piazza, Gabriele Pulcini, Matteo Tesi
Sequent-style refutation calculi with non-invertible rules are challenging to design because multiple proof-search strategies need to be simultaneously verified. In this paper, we present a refutation calculus for the multiplicative–additive fragment of linear logic ($\textsf{MALL}$) whose binary rule for the multiplicative conjunction $(\otimes )$ and the unary rule for the additive disjunction $(\oplus
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Some completeness results in derivational modal logic J. Log. Comput. (IF 0.7) Pub Date : 2023-08-09 Quentin Gougeon
Alongside the traditional Kripke semantics, modal logic also enjoys a topological interpretation, which is becoming increasingly influential. In this paper, we present various developments related to the topological derivational semantics, based on the Cantor derivative operator. We provide several characterizations of the validity of the axioms of bounded depth. We also elucidate the topological interpretation
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Computing minimal unsatisfiable core for LTL over finite traces J. Log. Comput. (IF 0.7) Pub Date : 2023-08-07 Tong Niu, Shengping Xiao, Xiaoyu Zhang, Jianwen Li, Yanhong Huang, Jianqi Shi
In this paper, we consider the minimal unsatisfiable core (MUC) problem for linear temporal logic over finite traces (LTL$_{f}$), which nowadays is a popular formal-specification language for AI-related systems. Efficient algorithms to compute such MUCs can help locate the inconsistency rapidly in the written LTL$_{f}$ specification and are very useful for the system designers to amend the flawed requirement
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A fuzzy structure processing mechanism for graph grammar J. Log. Comput. (IF 0.7) Pub Date : 2023-08-03 Yufeng Liu, Fan Yang, Jian Liu, Song Li
A strict graph-matching mechanism brings normativeness to graph grammar but leads to graph grammar insufficiency when processing fuzzy grammatical structures. To address this issue, the current paper proposes an improved formal framework for graph grammar that enables it to effectively specify the ambiguity of graph models while maintaining normativeness and intuition. First, the improved framework
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ECHO: A hierarchical combination of classical and multi-agent epistemic planning problems J. Log. Comput. (IF 0.7) Pub Date : 2023-07-24 Davide Soldà, Francesco Fabiano, Agostino Dovier
The continuous interest in Artificial Intelligence (AI) has brought, among other things, the development of several scenarios where multiple artificial entities interact with each other. As for all the other autonomous settings, these multi-agent systems require orchestration. This is, generally, achieved through techniques derived from the vast field of Automated Planning. Notably, arbitration in
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Prime spectrums of EQ-algebras J. Log. Comput. (IF 0.7) Pub Date : 2023-07-19 Bin Zhao, Wei Wang
The main purpose of this paper is to study prime spectrums of EQ-algebras and to solve two open problems about $\wedge $-prime spectrums of involutive and prelinear EQ-algebras, which were proposed by N. Akhlaghinia, R.A. Borzooei and M. A. Kologani. In order to do so, we first give some characterizations of preideals, prime preideals and maximal preideals on (good) EQ-algebras, respectively. Then
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4DL: a four-valued dynamic logic and its proof theory J. Log. Comput. (IF 0.7) Pub Date : 2023-07-18 Diana Costa
Transition systems are often used to describe the behaviour of software systems. If viewed as a graph then, at their most basic level, vertices correspond to the states of a program and each edge represents a transition between states via the (atomic) action labelled. In this setting, systems are thought to be consistent and at each state formulas are evaluated as either true or false. On the other
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Effective inseparability and some applications in meta-mathematics J. Log. Comput. (IF 0.7) Pub Date : 2023-06-20 Yong Cheng
Effectively inseparable pairs and their properties play an important role in the meta-mathematics of arithmetic and incompleteness. Different notions are introduced and shown in the literature to be equivalent to effective inseparability. We give a much simpler proof of these equivalences using the strong double recursion theorem. Then we prove some results about the application of effective inseparability
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Tractable depth-bounded approximations to FDE and its satellites J. Log. Comput. (IF 0.7) Pub Date : 2023-06-19 Marcello D’Agostino, Alejandro Solares-Rojas
FDE, LP and $\mathbf {K_{3}}$ are closely related to each other and admit of an intuitive informational interpretation. However, all these logics are co-NP complete, and so idealized models of how an agent can think. We address this issue by shifting to signed formulae, where the signs express imprecise values associated with two bipartitions of the corresponding set of standard values. We present
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Polyatomic logics and generalized Blok–Esakia theory J. Log. Comput. (IF 0.7) Pub Date : 2023-06-16 Rodrigo Nicolau Almeida
This paper presents a novel concept of a polyatomic logic and initiates its systematic study. This approach, inspired by inquisitive semantics, is obtained by taking a variant of a given logic, obtained by looking at the fragment covered by a selector term. We introduce an algebraic semantics for these logics and prove algebraic completeness. These logics are then related to translations, through the
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Master Surgical Scheduling via Answer Set Programming J. Log. Comput. (IF 0.7) Pub Date : 2023-06-13 Marco Mochi, Giuseppe Galatà, Marco Maratea
The problem of finding a Master Surgical Schedule (MSS) consists of scheduling different specialties to the operating rooms (ORs) of a hospital clinic. To produce a proper MSS, each specialty must be assigned to some ORs, where the number of assignments is different for each specialty and can also vary during the considered planning horizon. The problem is enriched by considering resource availability
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Two kinds of enriched topological representations of Q-algebras J. Log. Comput. (IF 0.7) Pub Date : 2023-06-09 Xianglong Ruan
In this paper, we continue the study of the enriched topological representation of $Q$-algebras where $Q$ is a unital quantale and give two kinds of enriched topological representations of $Q$-algebras. The first one is based on strong $M_3$-valued $Q$-algebra homomorphisms, and the second way is based on strong $M_6$-valued $Q$-algebra homomorphisms. For the first way, we first construct a spatial
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Implicit commitment in a general setting J. Log. Comput. (IF 0.7) Pub Date : 2023-06-09 Mateusz ŁeŁyk, Carlo Nicolai
Gödel’s Incompleteness Theorems suggest that no single formal system can capture the entirety of one’s mathematical beliefs, while pointing at a hierarchy of systems of increasing logical strength that make progressively more explicit those implicit assumptions. This notion of implicit commitment motivates directly or indirectly several research programmes in logic and the foundations of mathematics;
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Constraint propagation on GPU: A case study for the AllDifferent constraint J. Log. Comput. (IF 0.7) Pub Date : 2023-06-08 Fabio Tardivo, Agostino Dovier, Andrea Formisano, Laurent Michel, Enrico Pontelli
The AllDifferent constraint is a fundamental tool in Constraint Programming. It naturally arises in many problems, from puzzles to scheduling and routing applications. Such popularity has prompted an extensive literature on filtering and propagation for this constraint. This paper investigates the use of General Processing Units (GPUs) to accelerate filtering and propagation. In particular, the paper
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A logical framework to model software development by multiple agents following a common specification J. Log. Comput. (IF 0.7) Pub Date : 2023-06-08 Georgios V Pitsiladis, Petros S Stefaneas
In this paper, we address modelling program development by multiple different programmers (or programming teams) who work in different settings (programming languages or reasoning frameworks) but follow a common specification. After consideration of some philosophical issues regarding program development, including its similarities and dissimilarities with scientific theorizing, we extend a logical
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Some techniques for reasoning automatically on co-inductive data structures J. Log. Comput. (IF 0.7) Pub Date : 2023-06-08 Nicolas Peltier
Some techniques are proposed for reasoning on co-inductive structures. First, we devise a sound axiomatization of (conservative extensions) of such structures, thus reducing the problem of checking whether a formula admits a co-inductive model to a first-order satisfiability test. We devise a class of structures, called regularly co-inductive, for which the axiomatization is complete (for other co-inductive
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Permissive and regulative norms in deontic logic J. Log. Comput. (IF 0.7) Pub Date : 2023-06-01 Maya Olszewski, Xavier Parent, Leendert Van der Torre
This article provides a systematic analysis of the well-known notions of weak and strong permission in input/output (I/O) logic. We extend the account of permission initially put forward by Makinson and Van der Torre to the whole family of I/O systems developed during the last two decades. The main contribution is a series of characterization results for strong permission, based on establishing the
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Kettle logic in abstract argumentation J. Log. Comput. (IF 0.7) Pub Date : 2023-05-26 Timotheus Kampik
Kettle logic is a colloquial term that describes an agent’s advancement of inconsistent arguments in order to defeat a particular claim. Intuitively, a consistent subset of the advanced arguments should exist that is at least as successful at refuting the claim as the advancement of the set of inconsistent arguments. In this paper, we formalize this intuition and provide a formal analysis of kettle
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Nonmonotonic inferences: Classical conclusions in an intuitionistic modal framework J. Log. Comput. (IF 0.7) Pub Date : 2023-05-09 Gisèle Fischer Servi
We introduce a conceptual foundation for nonmonotonic reasoning which integrates an intuitionistic plurimodal logic with classical logic. The need for a multilogical system arises once we understand that to legitimately infer less than certain conclusions, we make two different kinds of assessments: an external one (what are the alternatives) and an internal one (which logic should govern the set of
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A new perspective on completeness and finitist consistency J. Log. Comput. (IF 0.7) Pub Date : 2023-04-24 Paulo Guilherme Santos, Wilfried Sieg, Reinhard Kahle
In this paper, we study the metamathematics of consistent arithmetical theories $T$ (containing $\textsf {I}\varSigma _{1}$); we investigate numerical properties based on proof predicates that depend on numerations of the axioms. Numeral Completeness. For every true (in $\mathbb {N}$) sentence $\vec {Q}\vec {x}.\varphi (\vec {x})$, with $\varphi (\vec {x})$ a $\varSigma _{1}(\textsf {I}\varSigma _1)$-formula
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Scheduling pre-operative assessment clinic with answer set programming J. Log. Comput. (IF 0.7) Pub Date : 2023-04-12 Simone Caruso, Giuseppe Galatà, Marco Maratea, Marco Mochi, Ivan Porro
The problem of scheduling pre-operative assessment clinic (PAC) consists of assigning patients to a day for the exams needed before a surgical procedure, taking into account patients with different priority levels, due dates and operators availability. Realizing a satisfying schedule is of upmost importance for a hospital, since delay in PAC can cause delay in the subsequent phases, thus lowering patients’
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A formal, diagrammatic, and operational study of normative relations J. Log. Comput. (IF 0.7) Pub Date : 2023-04-04 Matteo Pascucci, Giovanni Sileno
In this work, we provide an extensive analysis of Hohfeld’s theory of normative relations, focusing in particular on diagrammatic structures. Our contribution is threefold. First, we specify an extensional formal language to represent the main notions in the two families of normative relations identified by Hohfeld (i.e. the deontic and the potestative family). Our primary focus is on the part of the
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Incrementally predictive runtime verification J. Log. Comput. (IF 0.7) Pub Date : 2023-03-31 Angelo Ferrando, Giorgio Delzanno
Runtime verification is a lightweight formal verification technique used to verify the runtime behaviour of software (resp. hardware) systems. Given a formal property, one or more monitors are synthesized to verify the latter against a system execution. A monitor can only conclude the violation of a property when it observes such a violation. Unfortunately, in safety-critical scenarios, this might
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Sustainable goal-oriented smart environments: a declarative programming approach J. Log. Comput. (IF 0.7) Pub Date : 2023-03-29 Giuseppe Bisicchia, Stefano Forti, Antonio Brogi
The sustainable management of smart environments enabled by the Internet of Things (IoT) requires new methodologies and tools to suitably handle potentially many users and their objectives on cyber-physical systems, e.g. smart lighting, smart A/C. In this article, we propose a declarative framework to model IoT-enabled smart environments. Our methodology permits (i) expressing user roles and hierarchical
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Tame and full strict-Π11 reflection: A proof-theoretic approach J. Log. Comput. (IF 0.7) Pub Date : 2023-03-21 Gerhard Jäger
Strict-$\varPi ^{1}_{1}$ reflection is an important principle that is discussed in detail, e.g. in Barwise [ 2]. Whereas Barwise puts his focus on the importance of strict-$\varPi ^{1}_{1}$ formulas for generalized recursion theory and definability theory, we choose a proof-theoretic approach.
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There are no minimal essentially undecidable theories J. Log. Comput. (IF 0.7) Pub Date : 2023-03-20 Juvenal Murwanashyaka, Fedor Pakhomov, Albert Visser
We show that there is no theory that is minimal with respect to interpretability among recursively enumerable essentially undecidable theories.
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Modelling Supra-Classical Logic in a Boltzmann Neural Network: II Incongruence J. Log. Comput. (IF 0.7) Pub Date : 2023-03-11 Glenn Blanchette, Anthony Robins
Information present in any training set of vectors for machine learning can be interpreted in two different ways, either as whole states or as individual atomic units. In this paper, we show that these alternative information distributions are often inherently incongruent within the training set. When learning with a Boltzmann machine, modifications in the network architecture can select one type of
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Non-distributive positive logic as a fragment of first-order logic over semilattices J. Log. Comput. (IF 0.7) Pub Date : 2023-03-01 Jim de Groot
We characterize non-distributive positive logic as the fragment of a single-sorted first-order language that is preserved by a new notion of simulation called a meet-simulation. Meet-simulations distinguish themselves from simulations because they relate pairs of states from one model to single states from another. En route to this result, we use a more traditional notion of simulations and prove a
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Completeness in partial type theory J. Log. Comput. (IF 0.7) Pub Date : 2023-02-20 Petr Kuchyňka, Jiří Raclavský
The present paper provides a completeness proof for a system of higher-order logic framed within partial type theory. The framework is a modification of Tichý’s extension of Church’s simple type theory, equipped with his innovative natural deduction system in sequent style. The system deals with both total and partial (multiargument) functions-as-mappings and also accommodates algorithmic computations
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Normal functions and maximal order types J. Log. Comput. (IF 0.7) Pub Date : 2023-02-17 Anton Freund, Davide Manca
Transformations of well partial orders induce functions on the ordinals, via the notion of maximal order type. In most examples from the literature, these functions are not normal, in marked contrast with the central role that normal functions play in ordinal analysis and related work from computability theory. The present paper aims to explain this phenomenon. In order to do so, we investigate a rich
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What do ultraproducts remember about the original structures? J. Log. Comput. (IF 0.7) Pub Date : 2023-02-01 Henry Towsner
We describe a syntactic method for taking proofs that use ultraproducts and translating them into direct, constructive proofs.
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Two 4-valued implicative expansions of first-degree entailment logic: The relevant logic BN4VSP and the (relevant) entailment logic BN4AP J. Log. Comput. (IF 0.7) Pub Date : 2023-01-31 Gemma Robles
A logic L has the ‘variable-sharing property’ (VSP) if in all L-theorems of the form $A\rightarrow B$, $A$ and $B$ share at least a propositional variable. A logic L has the ‘Ackermann property’ (AP) if in all L-theorems of the form $A\rightarrow (B\rightarrow C)$, $A$ contains at least a conditional connective ($\rightarrow $). Anderson and Belnap consider the VSP a necessary property of any relevant
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Argumentation Frameworks with Attack Classification J. Log. Comput. (IF 0.7) Pub Date : 2023-01-30 Alexandros Vassiliades, Giorgos Flouris, Theodore Patkos, Antonis Bikakis, Nick Bassiliades, Dimitris Plexousakis
argumentation frameworks (AAFs), introduced by Dung (1995, Artif. Intell., 228, 321–357), enabled a new way of reasoning with arguments, which does not take into account the internal structure of arguments but only how they are related to each other. The only form of relation considered in AAFs is a binary attack relation on the set of arguments. From the definitions of acceptability semantics of AAFs
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A Principle-based Account of Self-attacking Arguments in Gradual Semantics J. Log. Comput. (IF 0.7) Pub Date : 2023-01-28 Vivien Beuselinck, Jérôme Delobelle, Srdjan Vesic
The issue of how a semantics should deal with self-attacking arguments was always a subject of debate among argumentation scholars. A consensus exists for extension-based semantics because those arguments are always rejected (as soon as the semantics in question respects conflict-freeness). In case of gradual semantics, the question is more complex, since other criteria are taken into account. In this
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A comprehensive account of the burden of persuasion in abstract argumentation J. Log. Comput. (IF 0.7) Pub Date : 2023-01-27 Timotheus Kampik, Dov Gabbay, Giovanni Sartor
In this paper, we provide a formal framework for modeling the burden of persuasion in legal reasoning. The framework is based on abstract argumentation, a frequently studied method of non-monotonic reasoning, and can be applied to different argumentation semantics; it supports burdens of persuasion with arbitrary many levels, and allows for the placement of a burden of persuasion on any subset of an
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Proof theory for the logics of bringing-it-about: Ability, coalitions and means-end relationship J. Log. Comput. (IF 0.7) Pub Date : 2023-01-23 Tiziano Dalmonte, Charles Grellois, Nicola Olivetti
The logic of bringing-it-about (BIAT) aims to capture a notion of agency in which actions are analysed in terms of their results: ‘An agent does something’ means that the agent brings it about that something takes place. Our starting point is the basic BIAT logic as introduced by Elgesem in the ‘90s: this logic contains only a modal operator to express BIAT statements by single agents. Several extensions
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Handling support cycles and collective interactions in the logical encoding of higher-order bipolar argumentation frameworks J. Log. Comput. (IF 0.7) Pub Date : 2023-01-20 Marie-Christine Lagasquie-Schiex
In our paper [17], we have proposed a logical encoding of argumentation frameworks with higher-order interactions (i.e. attacks or supports whose targets are arguments or other attacks or supports) with an evidential interpretation for supports, such frameworks are called REBAF. With this encoding, we are able to characterize the semantics of REBAF under the form of specific logical models. Nevertheless
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On all pure three-valued logics J. Log. Comput. (IF 0.7) Pub Date : 2022-12-14 Federico Pailos
We investigate the class of all pure three-valued logics that result from choosing the eight subsets of $\{0, 1, \frac {1}{2}\}$ as designated values on the strong Kleene schema, including the sets that are not (order) filters. We present some of their main characteristics and show some formal relations between these logics. We also suggest a recipe to build philosophical interpretations for most of
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Soundness and Completeness Results for LEA and Probability Semantics J. Log. Comput. (IF 0.7) Pub Date : 2022-12-07 Eoin Moore
In Artemov (2020, J. Logic Comput., 30, 61–76), a logical system called the logic of evidence aggregation (LEA) was introduced, along with an intended semantics for it called probability semantics. The goal was to describe probabilistic evidence aggregation in the setting of formal logic. However, as noted in that paper, LEA is not complete with respect to probability semantics. This leaves the tasks